M000000230

$$\pi=64\arctan\left(\frac{1}{21}\right)+12\arctan\left(\frac{1}{239}\right)+16\arctan\left(\frac{1}{353}\right)+16\arctan\left(\frac{1}{21637}\right)$$
Compact formula64[21] + 12[239] + 16[353] + 16[21637]
Lehmer's measure1.79992
References
Wetherfield, Michael Roby and Chien-Lih, Hwang. Computing pi: Lists of Machin-type (inverse cotangent) identities for pi/4, [Online; accessed 04-February-2024], 2013. [web.archive.org/web/20240204042153/http] [Found by Amrik Singh Nimbran on 29 June 2009.]